It is possible, but unlikely. In property damage cases, most police avoid giving tickets as it is just more hassle for them. Obviously, since you didn't have coverage at the time, your best bet is to have the lady get 2 estimates and if they look fair, offer to pay the lower of them. If she won't accept, try to work out some deal in between the 2. Otherwise, there are not many options except waiting to get sued by her or her carrier and cutting a deal then, which could risk your driver's license under the Safety and Financial Responsibility Law.
Best option is to contact her asking for estimates.
Stephen L. Hoffman
Law Office of Stephen L. Hoffman LLC
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I agree with Mr. Hoffman, getting a ticket is unlikely. Depending on the cost of the repairs, you may consider hiring a lawyer to document the settlement. If the cost of repairs are very minor, you may be willing to bear the risk of not having a lawyer draft the settlement agreement and release.
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Technically in Texas you can still get a ticket after the accident but probably not likely to happen. However, I have had two different clients who had tickets mailed to them from different jurisdictions for accidents that occurred months earlier.